Probability 1 Question 11
19. The probability that $x _1+x _2+x _3$ is odd, is
(a) $\frac{29}{105}$
(b) $\frac{53}{105}$
(c) $\frac{57}{105}$
(d) $\frac{1}{2}$
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Answer:
Correct Answer: 19. (b)
Solution:
- PLAN Probability $=\frac{\text { Number of favourable outcomes }}{\text { Number of total outcomes }}$
As, $x _1+x _2+x _3$ is odd.
So, all may be odd or one of them is odd and other two are even.
$\therefore$ Required probability
$$ \begin{aligned} & { }^{2} C _1 \times{ }^{3} C _1 \times{ }^{4} C _1+{ }^{1} C _1 \times{ }^{2} C _1 \times{ }^{4} C _1+{ }^{2} C _1 \times{ }^{2} C _1 \times{ }^{3} C _1 \\ & =\frac{{ }^{1} C _1 \times{ }^{3} C _1 \times{ }^{3} C _1}{{ }^{3} C _1 \times{ }^{5} C _1 \times{ }^{7} C _1} \\ & =\frac{24+8+12+9}{105} \\ & =\frac{53}{105} \end{aligned} $$
